Wormholes generated by a density-gradient dependent equation of state in f(R,Lm,T) gravity

In this work, Static wormhole models are examined within the framework of curvature-based f ( R , L m , T ) gravity theory. A relationship between the matter energy density and pressure is proposed for the Morris-Thorne wormhole geometry with a constant redshift function. By incorporating a gradient-dependent equation of state ( P r = P r ( ρ , ρ ′ ) and P t = P t ( P r , P r ′ ) ), we derive exact wormhole solutions for two representative cases. Our analysis shows that exact wormhole models can admit null energy condition violations localized at the throat, while preserving a non-negative matter energy density. The stability analysis is performed via the Tolman–Oppenheimer-Volkoff equation under hydrostatic equilibrium, demonstrating that the balance among anisotropic and hydrostatic forces sustains the wormhole’s stable configuration. For positive and negative values of ζ , the energy flux attains a pronounced negative magnitude, inducing an outward flux that supports the stability of the wormhole throat. The geometric characteristics of the wormhole are examined through embedding diagrams, and the total exotic matter required to maintain the configuration is evaluated using the volume integral quantifier. Simultaneously, the effective potential demonstrates enhanced photon confinement and increased stability of particle orbits.